Edit: The model isn't the Stargazer in Picard's ready room it's the NCC-7100. So it could be the right color for that ship if it was a new technology testbed.

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We have seen further tabletop models that weren't the right color for the ship they depict. Most of the Constitution models aboard the E-D were painted bright silver, say. I guess a model in the Captain's very own Ready Room might be more accurate than mere mass-produced tabletop decorations elsewhere, but that need not really be the case.

Does a Constellation class ship with the registry NCC-7100 really exist? Or is the number just an in-joke by the person who gave Picard that model - perhaps the door number to a very specific suite, or a stardate of great significance? We can't really tell - but we can tell that the tabletop model differs from the Stargazer in all sorts of detail, in addition to the registry and the color...

Then again, we can only tell that when we look really close, and that is cheating, because none of the episodes show the model closely enough. Only set photography reveals e.g. the lack of secondary phaser turrets or certain ventral detail.